The distinction between our two regularizations mirrors
that between toric geometry and matroid theory. In statistics, this is the
distinction between toric models and linear models [1]}.
These objects are central in the study of positive geometries
in combinatorics and physics (cf. [2]}).
In Section  we develop a comparative theory.
After a review of known facts in Proposition REF  and REF ,
we present our findings in Theorem REF 
and REF . They concern the algebraic curves and positive varieties
arising from linear programming.
